few_shots: Example:
Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Standard options: 
A. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
B. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
C. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (Expectations for unit rates in this grade are limited to non-complex fractions.)


Thought: This problem solves a real-world problem involving mixing ingredients for cookies. A student doing this problem would need to reason about equivalent ratios of butter amounts to sugar amounts.
Answer: B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_000972

6
options: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

Verify experimentally the properties of rotations, reflections, and translations:
- Lines are taken to lines, and line segments to line segments of the same length.
- Angles are taken to angles of the same measure.
- Parallel lines are taken to parallel lines.
problem_activity: Warm-up
Polygons are special shapes because once we know the vertices, listed in order, we can join them by line segments to produce the polygon. This is important when performing rigid transformations. Because rigid transformations take line segments to line segments, once we track where the vertices of a polygon go, we can join them in the correct order with segments to find the image of the polygon.
In this warm-up, students begin to explore this structure, finding corresponding points in congruent polygons which are
not
vertices.
Launch
Give 3 minutes quiet think time followed by 2 minutes for a whole-class discussion.
Student Facing
Trapezoids
\(ABCD\)
and
\(A’B’C’D’\)
are congruent.
Draw and label the points on
\(A’B’C’D’\)
that correspond to
\(E\)
and
\(F\)
.
Draw and label the points on
\(ABCD\)
that correspond to
\(G’\)
and
\(H’\)
.
Draw and label at least three more pairs of corresponding points.
[IMG]
Student Response
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Anticipated Misconceptions
Students may struggle to find corresponding points that are not vertices. Suggest that they use tracing paper or the structure of the grid to help identify these corresponding points.
Activity Synthesis
Remind students that when two figures are congruent, every point on one figure has a corresponding point on the other figure.
Ask students what methods they used to find their corresponding points. Possible answers include:
Using the grid and the corresponding vertices to keep track of distances and place the corresponding point in the right place
Using tracing paper and rigid motions taking one polygon to the other


correct_option_index: 0